Jacobian conjecture

Let F:nn be a polynomial map, i.e.,


for certain polynomialsPlanetmathPlanetmath fi[X1,,Xn].

If F is invertiblePlanetmathPlanetmathPlanetmathPlanetmath, then its Jacobi determinant det(fi/xj), which is a polynomial over , vanishes nowhere and hence must be a non-zero constant.

The Jacobian conjecture asserts the converseMathworldPlanetmath: every polynomial map nn whose Jacobi determinant is a non-zero constant is invertible.

Title Jacobian conjecture
Canonical name JacobianConjecture
Date of creation 2013-03-22 13:23:46
Last modified on 2013-03-22 13:23:46
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 5
Author PrimeFan (13766)
Entry type Conjecture
Classification msc 14R15
Synonym Keller’s problem